Hello,
I am creating a blog,
on the front page the content of the post is displayed fully, but when you click on a category like Quotes About Life the facebook icons dissapear because it is displayed to not show full content of posts in Category view.

You can configure it from Suffusion Options → Layouts → Category Views, but I believe the issue is with your plugin not showing the icons on category pages. Your categories are set up to show full content as of now.